ML20125E662
| ML20125E662 | |
| Person / Time | |
|---|---|
| Site: | Hope Creek  |
| Issue date: | 05/31/1985 |
| From: | Henrie D GENERAL ELECTRIC CO. |
| To: | |
| Shared Package | |
| ML20125E587 | List: |
| References | |
| NUDOCS 8506130191 | |
| Download: ML20125E662 (11) | |
Text
O APPROXIMATION OF INSTRUCTURE RRS USING INPUT RESPONSE SPECTRA AND
-TRANSMISSIBILITIES OBTAINED FROM TEST l
f BY DONALD K. HENRIE
~
~CENERAL ELECTRIC COMPANY MAY, 1985 4
A
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ABSTRACT l Significant margin exists between test response spectra (TRS) and the associ- '
ated required response spectra (RRS) for many dynamic tests performed for the dynamic qualification of Class 1 electrical and me.chanical equipment. ]
This paper presents a simplified, conservative methodology for obtaining upper !
bound in-structure RRS which envelop the actual service condition RRS. The methodology is applicable for both seismic and nonseismic input motion re-sponse spectra. The methodology utilizes the . test input floor RRS and the transmissibilities obtained from the resonance search part of the dynamic test. ;
i The advantages of the simplified methodology are reduced expenditures in both engineering manhours and computer costs.
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TABLE OF CONTENTS W
1.0 INTRODUCTION
1 2.0 RESdNANCE SEARCH INPUT MOTION - INPUT AND 1 RESPONSE RRS AMPLIFICATION CONTENT 3.0 RANDOM INPUT MOTION - INPUT AND RESPONSE 4 RRS AMPLIFICATION CONTENT
4.0 CONCLUSION
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4 FIGURES '
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. .. - . . . . . . . . . . . . . . h l
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1.0 INTRODUCTION
The purpose of this paper is to present a simplified methodology for obtaining upper bound required response spectra (RRS) at in-structure equipment mounting locations for equipment attsched to intermediats support structures. Typical ,
examples of intermediste support structures include equipment control panels and local racks. !
Equipment components mounted in control panels or local racks have generally, !
in the'past, been qualified by testing the entire panel or local rack assen- l bly. If a component or device was moved to a new location within the assen-bly, the entire assembly would generally have to be retested to qualify the component or device for the new configuration.
l A much more cost effective qualification procedure is to test the individual components or devices as opposed to the entire assembly. The tested com-ponents are then qualified for any in-structure location as long as the TRS envelops the in-structure location RRS.
When individual components are tested, there is typically a significant margin between the TRS and any given in-structure RRS. This is due to the inherent ruggedness and durability of individual components and the fact that generic
- tests are generally performed. Consequently, due to the TRS margin relative to the RRS, it is possible to dynamically qualify a significant number of devices and components by applying simplified methods in the generation of conservative, upper-bound RRS which are, never-the-less, enveloped 'by the individual component test TRS.
It should also be noted that whenever TRS are generated at individual in-structure locations for tests performed on entire assemblies, a device mounted at a given in-structure location is qualified to the TRS at that location.
2.0 RESONANCE SEARCH INPUT MOTION - INPUT AND RESPONSE RRS AMPLIFICATION CONTENT A typical equipment intermediate support structure such as a control panel or local rack is depicted in Figure 1. In-structure degree-of-freedom (DOF) "i" corresponds to any device mounting location. The base input motion is denoted by Y,(t). _
\
In the past, safety related devices attached at in-structure DOF's i (i = 1, l
t 2 ..., n) were qualified by testing the entire assembly. In such a test,
! only the base input motion (i.e., table control motion) was monitored. If the control motion test response spectra (TRS) adequately enveloped the test input motion required response spectra (RRS), all devices mounted in the assembly were qualified. In general, if device mounting locations were interchanged, the entire assembly would have to be retested to qualify the devices for the new configur'stion.
Alternatively, if the RRS at the device mounting locations were known, the individual devices could be generically tested one time only. A device would i then be qualified for any location if the generic TRS for that device envel-l ope.1 the RRS correspor. Jing to its location.
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- Harmonic Leinulod_ial) base input motion with driving frequency 0 and peak amplitude IPA, (see Figure 2(a)) can be represented by h,(t)=ZPA,sinQt ... (2.1)
The maximum value of the dynamic magnification factor (DNF) for the response of a simple harmonic oscillator (SHO), with natural frequency w, subjected to such a base input motion is given by 1
(DMF) = ... (2.2)
(1-0 /w ) +-(2AD/w)
For the resonant condition; D/w = 1. Equation (2.2) becomes 1
(DMF) = ... (2.3) 2A where A is 4he critical damping ratio, i.e., A = C/Cc.
At present there are three markedly different test procedures for performing the resonance search to determine the eigen characteristic of any assembly to be qualified by dynamic testing. The input motions corresponding to the three are: 1) sinusodial sweep. 2) random, and 3) impulsive. The transmissibil-ities utilized in the presentation correspond to the sinusodial sweep.
4 In a sinusodial sweep, the test specit:en is subjected to sinusodial excitation in which the sinusoid frequency is slowly varied through a range of fre-quencies. If the frequency sweep rate is sufficiently slow, the transmissi-bilities obtained are identical to those that would be obtained by "dvelling" ~
at a sequence of discrete frequencies. In other words, the sweep rate must be sufficiently slow to allow for the resonant build-up.
Thus searchthe baseThen, test. input referrin motion Tl(t) of Figure to Figure 1 is 2(b) andsinusodial Equation for (2.3),the resonance it follows )
that _
.M 8-i
= ... (2.4) 2A Bowever, the response at in-structure DOF i of Figure 1, will not be exactly harmonic since, in general, more than one mode will be driven at the base input motion
- driving frequency. Then, referring to Figure 2(d), we can write i
A g< ... (2.5) 2A Gmmo &
If the RRS for the base input motion and for the response at in-structure DOF
- i are for the same oscillator damping, we can divide Equation (2.5) by the respective sides of Equation (2.4) to yield T, < I, x ( 1) ... (2.6) 3A, l
We can also write YFA'1 - IFI, x ( *) ... (2.7)
ZPA, Recall from (b) and (d) of Figure 2, that T (u) is the RRS of the sinusodial base input motion and that T (W) is the RRS 8f the resulting acceleration time history response at in-strubure DOF i. Barred terms correspond to harmonic base-input motion as indicated in Figure 2. .
Let us next consider the amplification in A (W) and A m) at frequencies different than the driving frequency of the Earmonic exk(itation. Let a(s) denote the amplification associated with the spectral acceleration at fre-quency W relative to the ZPA for the harmonic (sinusodial) base input motion.
That is T s(w) . a(w) YF1 s ... (2.8)
Then, for the associated "not quite harmonic response".at in-structure DOF 1, we can write T (m) < a(s) YFIf . ... (2.9)
Equation (2.9) can now be divided by the respective sides of Equation (2.8) to yield 171 Ag (u) < T,(u) x ( I) ... (2.10)
ZPA, Equations (2.6), (2.7), and (2.10) cover the entire frequency range of inter-
- est. Thus 'for the. case of the base support harmonic (sinusodial) excitation given by Equation (2.1), the response RRS at in-structure DOF i is bounded by
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the RRS of the barmonic base input motion after it has been multiplied by the ratio (Wi g/N 1,). The ration 1 ... (2.11)
T=
FAe
l of the zero period accelerations of the response to input motions is defined as the transmissibility. Transmissibilities are obtained during the resonance search (sinusodial sweep) test for each of the eigen values of the test
" specimen"; i.e., for D = w), j = 1, ..., n, in Equation (2.1).
3.0 RANDOM INPUT MOTION - INPUT AND RESPONSE RRS AMPLIFICATION CONTENT As developed in the previous section, for the case of the base support har-monic excitation given by Equation (2.1), the response RRS at in-structure DOF i is bounded by the RRS of the harmonic base input motion af ter it has been multiplied by the transmissibility defined by Equation (2.11).
Theoretically, the maximum amplifications possible in a multi-degree-of-freedom system are those associated with harmonic excitations at the system natural frequencies. Such amplifications are, therefore, always greater than corresponding values associated with random input motion.
The transmissibilities defined by Equation (2.11) for 0 = w , where w (j = 1 .
... n) corresponds to the discrete eigen values, can then de written $as l T (m ) = ... (3.1)
) -
ZPA,(w )
The transmissibilities given by Equation (3.1) are obtained from the resonance search (sinusodial sweep) part of the dynamic test for each eigenvalue of the system (e.g., equipment control panels or local racks) being tested. For sufficiently slow sweep rates, the transmissibilities obtained from the resonance search are identical to corresponding results obtained by "dvelling" ,
at each eigen value w , j = 1, ... n.
Since the amplifications associated with (3.1) correspond to harmonic excita-tions at the system resonant frequencies and since they are theoretically the maximum possible, it follows that, for randor -itation. Equations (2.6),
(2.7), and (2.10) can be generalized and consolicated to yield A (# ) < A,(u ) x ( ) ... (3.2)
. ZPA,(w )
The randon input motion base input acceleration time histories and RRS are illustrated in Figure 3(a) and 3(b), respectively, and the response at in-structure DOF i in Figure 3(c) and 3(d).
4.0 CONCLUS, IONS For random excitation, the RRS at any in-structure DOF i is conservatively bounded by the RRS of the random base support input motion after it has been scaled, at each resonant frequency, by the transmissibilities obtained from the sinusodial sweep resonance search test. The bounding relationship is given by Equation (3.2) for the entire frequency range of interest.
O In the event that the sinusodial sweep test sweep rate is to fast, the trans-missibilities obtained will be less than corresponding values obtained from a sine dwell test. If such is the case, the sinusodial sweep transmissibilities should be scaled up by the maximum ratio of Transmissibility Sinusodial Dwell Transmissibility Sinusodial Sweep as obtained from the dynamic test before applying Equation (3.2).
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